Problem: Rewrite as a simplified fraction. ${1.\overline{38} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 138.3838...\\ 1x &= 1.3838...\end{align*}}$ Subtracting the two equations, we have: ${99x = 137}$ ${x = \dfrac{137}{99}} \text{or} {1 \dfrac{38}{99}}$